alinik
۱۲ مهر ۱۳۸۸, ۱۹:۴۱
Journal of Fluids and Structures 21 (2005) 561–577
A new tube/support impact model for heat exchanger tubes
M.A. Hassana,, D.S. Weaverb, M.A. Dokainishb
aMechanical Engineering Department, University of New Brunswick, Fredericton, Canada E3B 5A3
bDepartment of Mechanical Engineering, McMaster University, Hamilton, Ont., Canada L8S 4L7
Received 10 January 2005; accepted 31 July 2005
Available online 21 October 2005
Abstract
Heat exchanger tubes are often loosely supported at intermediate points by plates or flat bars. Flow-induced
vibrations result in fretting wear tube damage due to impacting and rubbing of tubes against their supports. Prediction
of tube response relies on modelling the nonlinear tube/support interaction. The evaluated response is used to predict
the resultant wear damage using experimentally measured wear coefficients. An accurate prediction of impact forces
and work rate is therefore paramount. The analytical models available in the open literature generally assume tube/
support contact occurs at a single point. In this paper, a computational algorithm is proposed to describe tube/support
impact considering a finite support width. The new model provides a means of representing tube/support contact as a
combination of edge and segmental contact. The proposed model utilizes a distributed contact stiffness to describe the
segmental contact. The formulation also incorporates a stick/slip friction model. The model developed is utilized to
simulate the dynamics of loosely supported tubes.
r 2005 Elsevier Ltd. All rights reserved.
Keywords: Impact; Heat exchangers; Finite elements method; Nonlinear dynamics
1. Introduction
Many industries, such as process and power plants, utilize high thermal efficiency shell and tube heat exchanger
designs. Performance requirements often dictate high coolant velocities and flexible tubes, which in turn may cause
tubes to experience excessive flow-induced vibrations. A great deal of research has been devoted to flow-induced
vibrations due to their practical significance (Paı¨doussis, 1982; Chen, 1991; Weaver et al., 2000; Pettigrew and Taylor,
2003). These research efforts have led to many improvements in understanding the mechanisms of flow-induced
vibrations.
Parameters that affect tube wear can be measured during wear tests. In practical cases, however, analytical techniques
are necessary to estimate these effects from flow and vibration information. These techniques mainly utilize the
nonlinear time-domain simulation of tube dynamics via the finite element method. This includes modelling the tube/
support contact and friction forces. Modelling contact, in general, is a complex task due to the unknown contact
interface and friction conditions. The solution of such problems involves complex searching algorithms and iterative
procedures. However, such a general approach is not feasible in a flow-induced vibrations study in which large time
ARTICLE IN PRESS
www.elsevier.com/locate/jfs
0889-9746/$ - see front matter r 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jfluidstructs.2005.07.016
Corresponding author.
E-mail address: hassanm@unb.ca (M.A. Hassan).
records are required to obtain meaningful response average parameters. In such cases, the nonlinearity is localized and
the contact region is reasonably defined. Based on this fact, several codes, such as VIBIC (Rogers and Pick, 1977; Fisher
et al., 1989), H3DMAP (Sauve´ and Teper, 1987; Morandin and Sauve´ , 1999), GERBOISE (Axisa et al., 1988)
and INDAP (Hassan et al., 2002, 2003) have been developed to simulate tube/support interaction. These codes have
been utilized in the analysis of multispan tubes under simulated fluid forces and have yielded reasonable response
and impact force results. The tube/support interaction models available in the open literature generally treat impact
by introducing a spring at the support node. This greatly simplifies the modelling and results in a very efficient
algorithm. Therefore, the support node is the only node that has to be monitored. In other words, the support is
assumed to be a knife-edge type of support. However, in reality the support has a finite width which may not be well
simulated using the traditional model because this model permits the tube to overlap with the support along the support
width, as long as the contact node is within the support space. In addition, it is not possible to investigate the local
distribution of contact pressure or the effect of the support width on tube dynamics and wear. Most of the published
models make these kinds of assumptions. One approach to overcome this deficiency is to perform tube/support
interaction computations by defining complex finite-length support geometries in terms of several contact locations
along the support width. The single-point impact algorithm must be applied at each support a number of times (equal to
the number of contact nodes per support). In addition, in the presence of significant axial motion (for example, in-plane
motion in a U-bend tube) the algorithm may fail to handle some of the designated contact nodes being moved out of the
support space.
A new tube/support impact model for heat exchanger tubes
M.A. Hassana,, D.S. Weaverb, M.A. Dokainishb
aMechanical Engineering Department, University of New Brunswick, Fredericton, Canada E3B 5A3
bDepartment of Mechanical Engineering, McMaster University, Hamilton, Ont., Canada L8S 4L7
Received 10 January 2005; accepted 31 July 2005
Available online 21 October 2005
Abstract
Heat exchanger tubes are often loosely supported at intermediate points by plates or flat bars. Flow-induced
vibrations result in fretting wear tube damage due to impacting and rubbing of tubes against their supports. Prediction
of tube response relies on modelling the nonlinear tube/support interaction. The evaluated response is used to predict
the resultant wear damage using experimentally measured wear coefficients. An accurate prediction of impact forces
and work rate is therefore paramount. The analytical models available in the open literature generally assume tube/
support contact occurs at a single point. In this paper, a computational algorithm is proposed to describe tube/support
impact considering a finite support width. The new model provides a means of representing tube/support contact as a
combination of edge and segmental contact. The proposed model utilizes a distributed contact stiffness to describe the
segmental contact. The formulation also incorporates a stick/slip friction model. The model developed is utilized to
simulate the dynamics of loosely supported tubes.
r 2005 Elsevier Ltd. All rights reserved.
Keywords: Impact; Heat exchangers; Finite elements method; Nonlinear dynamics
1. Introduction
Many industries, such as process and power plants, utilize high thermal efficiency shell and tube heat exchanger
designs. Performance requirements often dictate high coolant velocities and flexible tubes, which in turn may cause
tubes to experience excessive flow-induced vibrations. A great deal of research has been devoted to flow-induced
vibrations due to their practical significance (Paı¨doussis, 1982; Chen, 1991; Weaver et al., 2000; Pettigrew and Taylor,
2003). These research efforts have led to many improvements in understanding the mechanisms of flow-induced
vibrations.
Parameters that affect tube wear can be measured during wear tests. In practical cases, however, analytical techniques
are necessary to estimate these effects from flow and vibration information. These techniques mainly utilize the
nonlinear time-domain simulation of tube dynamics via the finite element method. This includes modelling the tube/
support contact and friction forces. Modelling contact, in general, is a complex task due to the unknown contact
interface and friction conditions. The solution of such problems involves complex searching algorithms and iterative
procedures. However, such a general approach is not feasible in a flow-induced vibrations study in which large time
ARTICLE IN PRESS
www.elsevier.com/locate/jfs
0889-9746/$ - see front matter r 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jfluidstructs.2005.07.016
Corresponding author.
E-mail address: hassanm@unb.ca (M.A. Hassan).
records are required to obtain meaningful response average parameters. In such cases, the nonlinearity is localized and
the contact region is reasonably defined. Based on this fact, several codes, such as VIBIC (Rogers and Pick, 1977; Fisher
et al., 1989), H3DMAP (Sauve´ and Teper, 1987; Morandin and Sauve´ , 1999), GERBOISE (Axisa et al., 1988)
and INDAP (Hassan et al., 2002, 2003) have been developed to simulate tube/support interaction. These codes have
been utilized in the analysis of multispan tubes under simulated fluid forces and have yielded reasonable response
and impact force results. The tube/support interaction models available in the open literature generally treat impact
by introducing a spring at the support node. This greatly simplifies the modelling and results in a very efficient
algorithm. Therefore, the support node is the only node that has to be monitored. In other words, the support is
assumed to be a knife-edge type of support. However, in reality the support has a finite width which may not be well
simulated using the traditional model because this model permits the tube to overlap with the support along the support
width, as long as the contact node is within the support space. In addition, it is not possible to investigate the local
distribution of contact pressure or the effect of the support width on tube dynamics and wear. Most of the published
models make these kinds of assumptions. One approach to overcome this deficiency is to perform tube/support
interaction computations by defining complex finite-length support geometries in terms of several contact locations
along the support width. The single-point impact algorithm must be applied at each support a number of times (equal to
the number of contact nodes per support). In addition, in the presence of significant axial motion (for example, in-plane
motion in a U-bend tube) the algorithm may fail to handle some of the designated contact nodes being moved out of the
support space.